\( 6 y+2<-4 \) and \( -4(2 y+3)<-68 \) Solution Interval Notation

To solve the system of inequalities: 1. \( 6y + 2 < -4 \) 2. \( -4(2y + 3) < -68 \) **Step 1: Solve the first inequality** \[ 6y + 2 < -4 \] Subtract 2 from both sides: \[ 6y < -6 \] Divide by 6: \[ y < -1 \] **Step 2: Solve the second inequality** \[ -4(2y + 3) < -68 \] First, distribute the -4: \[ -8y - 12 < -68 \] Add 12 to both sides: \[ -8y < -56 \] Divide by -8 (remember to reverse the inequality sign when dividing by a negative number): \[ y > 7 \] **Step 3: Combine the solutions** The system of inequalities requires both conditions to be true simultaneously: \[ y < -1 \quad \text{and} \quad y > 7 \] However, there is no real number \( y \) that is both less than \(-1\) and greater than \(7\) at the same time. **Conclusion:** There is **no solution** to this system of inequalities. **Interval Notation:** \[ \emptyset \]